Scientists studied 9,000 pregnant women who received the flu shot and found that the rate of birth defects in their babies was 2 percent, identical to the rate among 77,000 pregnant women who were not vaccinated. The study was published in the journal Obstetrics & Gynecology.

Interestingly, women who received a flu shot were less likely to suffer a stillbirth. It's not clear why, but lead researcher Jeanne Sheffield of the University of Texas Southwestern Medical Center suspects the vaccine might help by preventing severe cases of flu.

Despite recommendations to get the flu shot, most pregnant women do not. In the U.S., only between 10 percent and one-quarter of women have been vaccinated each flu season over the last couple decades, Sheffield's team notes.

Based on studies, that seems largely due to safety worries.

On the other hand, Sheffield said "it's amazing" how many women are unaware that the flu itself is considered a risk during pregnancy.

"The flu is a problem in pregnancy," she said. "But we have a vaccine to prevent it. And it's considered safe and effective in any trimester."